Program transformations using temporal logic side conditions

This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program

Simplifying Inductive Schemes in Temporal Logic

In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula

Verifying Safety Properties With the TLA+ Proof System

TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and non-linear proof construction and verification, and it is independent of any verification tool or strategy. A Proof Manager uses backend verifiers such as theorem provers, proof assistants, SMT solvers, and decision procedures to check TLA+ proofs. This paper documents the first public release of TLAPS, distributed with a BSD-like license. It handles almost all the non-temporal part of TLA+ as well as the temporal reasoning needed to prove standard safety properties, in particular invariance and step simulation, but not liveness properties

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing

Formal verification of concurrent programs

Interactive theorem proving provides a general approach to modeling and verification of both finite-state and infinite-state systems but requires significant human efforts to deal with many tedious proofs. On the other hand, model-checking is limited to some application domain with small finite-state space. A natural thought for this problem is to integrate these two approaches. To keep the consistency of the integration and ensure the correctness of verification, we suggest to use type theory based theorem provers (e.g. Lego) as the platform for the integration and build a model-checker to do parts of the verification automatically. We formalise a verification system of both CCS and an imperative language in the proof development system Lego which can be used to verify both finite-state and infinite-state problems. Then a model-checker, LegoMC, is implemented to generate Lego proof terras for finite-state problems automatically. Therefore people can use Lego to verify a general problem with some of its finite sub-problems verified by LegoMC. On the other hand, this integration extends the power of model-checking to verify more complicated and infinite-state models as well. The development of automatic techniques and the integration of different reasoning methods would directly benefit the verification community. It is expected that further extension and development of this verification environment would be able to handle real life systems. On the other hand, the research gives us some experiences about how to automate proofs in interactive theorem provers and therefore will improve the usability and applicability of the theorem proving technology